Homework Help:
A yo-yo pulled by a rope: limit angle for the yo-yo to go to the left or to the right

1. The problem statement, all variables and given/known data
We have a yo-yo, formed by a little cylinder tied to a little rope, and two big disks as wheels, one for each side of the central cylinder. We do a force T on the rope; its slope is an angle θ over the horizontal x-axis.
We are given the mass m of the cylinder, the mass M of each wheel, the radius of the cylinder R1 and the radius of each wheel R2. We want to know the limit angle θ , for the acceleration to be positive or negative.
I try to explain it better: under a certain angle, the yo-yo have a pure roll in the positive direction, over this angle it goes "back" and rolls towards the negative direction.